Bendtner moved to north London from Copenhagen’s youth set-up in 2004, at the age of 16, but struggled to make an impact on the first team in the shadow of Robin van Persie.
The Dane, who scored 47 goals in 171 appearances for the Gunners, has spent two of the last three seasons on loan at Sunderland and Juventus.
South Korea striker Ju Young Park, another coming to the end of his contract, will also depart while Sweden midfielder Kim Kallstrom and Italian goalkeeper Emiliano Viviano’s loan spells will conclude.
France full-back Bacary Sagna, Poland keeper Lukasz Fabianski and young forward Zak Ansah have all moved on to Manchester City, Swansea and Charlton respectively.
Academy players Chuks Aneke, Daniel Boateng, Zach Fagan and Leander Siemann also leave the Emirates having reached the end of their current agreements.
A club statement said: "Everyone at Arsenal would like to take this opportunity to thank all of these players for their contribution to the club, and to wish them well for the future."